HOW TO WRITE EACH EXPRESSION AS A PRODUCT OF ITS FACTORS

List all the Factors of the monomial expression

Problem 1 :

Solution :

Decompose each expression into prime factors.

Finding the degree, coefficient and variables of following monomial expression

Variables :

The variables are the letters present in a monomial. That is, x, y, z,.. 

Coefficient :

The coefficient is the number that is multiplied by the variables. That is, 12x, 12y,..

Degree :

The degree is the sum of the exponents of the variables in a monomial.

That is, 12xy ---> Exponent of x is 1, Exponent of y is 1

So, the degree is 1 + 1 = 2

Problem 2 :

Solution :

Find the Greatest Common Factors of the following Monomial expression

Problem 3 :

12m²n³, 70m³n

Solution :

Find the GCF of 12m²n³, 70m³n.

12m²n³ = 2 ∙ 2 ∙ 3 ∙ m ∙ m ∙ n ∙ n ∙ n

70m³n = 2 ∙ 5 ∙ 7∙ m ∙ m ∙ m ∙ n

= 2 ∙ m ∙ m ∙ n

GCF = 2m²n

Problem 4 :

72a³b², 86a

Solution :

Find the GCF of 72a³b², 86a.

72a³b² = 2 ∙ 2 ∙ 2 ∙ 3 ∙ 3 . a ∙ a ∙ a ∙ b ∙ b

86a = 2 ∙ 43 ∙ a

GCF = 2a

Problem 5 :

44m²n, 48mn²

Solution :

Find the GCF of 44m²n, 48mn².

44m²n = 2 ∙ 2 ∙ 11 ∙ m ∙ m ∙ n

48mn² = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3 ∙ m ∙ n ∙ n

 = 2 ∙ 2 ∙ m ∙ n

GCF = 4mn

Problem 6 :

a²b³, ab³

Solution :

a²b³ = a ∙ a ∙ b ∙ b ∙ b

ab³ = a ∙ b ∙ b ∙ b

= a ∙ b ∙ b ∙ b

GCF = ab³

Problem 7 :

3x, 7xy²

Solution:

3x = 3 ∙ x

7xy² = 7 ∙ x ∙ y ∙ y 

GCF = x

Problem 8 :

4rs², 27st³

Solution:

4rs² = 2 ∙ 2 ∙ r ∙ s ∙ s

27st³ = 3 ∙ 3 ∙ 3 ∙ s ∙ t ∙ t ∙ t

GCF = s

Problem 9 :

18wx², 45wx

Solution:

18wx² = 2 ∙ 3 ∙ 3 ∙ w ∙ x ∙ x

45wx = 3 ∙ 3 ∙ 5 ∙ w ∙ x

= 3 ∙ 3 ∙ w ∙ x

GCF = 9wx

Problem 10 :

12y², 15y³, 5y

Solution:

12y² = 2 ∙ 2 ∙ 3 ∙ y ∙ y

15y³ = 3 ∙ 5 ∙ y ∙ y ∙ y

5y = 5 ∙ y

GCF = y

Problem 11 :

rs³, s³t, r²st²

Solution :

rs³ = r ∙ s ∙ s ∙ s

s³t = s ∙ s ∙ s ∙ t

r²st² = r ∙ r ∙ s ∙ t ∙ t

GCF = s